BAGHDAD (AP) – Iran agreed Sunday to attend a major regional conference on Iraq set for this week in Egypt – a major break as Iraq seeks support from its neighbors in quelling its sectarian violence.

The meeting, which will include both Iran’s foreign ministry and Secretary of State Rice, raised the possibility of a rare direct encounter between high-level American and Iranian officials.

“I will not rule out that we may encounter one another,” Ms. Rice told ABC’s “This Week.” “But what do we need to do? It’s quite obvious. Stop the flow of arms to foreign fighters. Stop the flow of foreign fighters across the borders.”

America accuses Iran of funding and arming the Shiite militias that are responsible for much of Iraq’s sectarian violence, and the Shiite-led Iraqi government has struggled to maintain good relations with Iran while not angering the Americans.

But those alleged militia links have also prompted numerous American politicians and analysts to urge the Bush administration to seek Iran’s help in curbing the violence in Iraq.

A statement from the Iraqi prime minister’s office said President Ahmadinejad telephoned the Iraqi leader and told him Iran would participate in the meeting Thursday and Friday in the resort of Sharm El-Sheik.

Iraq’s other neighbors as well as Egypt, Bahrain and representatives of the big five U.N. Security Council members have agreed to attend the meeting in Egypt, and the Shiite-led Iraqi government has been pressing for Iranian participation as well.

Mr. al-Maliki’s government also will face demands by Arab countries, most of which are Sunni-led, that it do more to accommodate disgruntled Sunni Arabs before pledging any substantial aid, according to a document obtained by The Associated Press. The Iranian Foreign Ministry spokesman Mohammad Ali Hosseini said Ali Larijani, the top Iranian envoy, would be in Baghdad on Sunday to discuss the conference with Iraqi government officials as Iran has “some questions and ambiguities about the agenda.”

The government in Tehran has demanded the release of five Iranian officials detained in the northern Iraqi city of Irbil by American troops in January, but Hosseini denied his country had linked its participation at the conference to that demand.

Iran says the official were diplomats who should not have been detained. The American military has said the Iranians are suspected of links to a network supplying arms to Iraqi insurgents – an accusation that Iran has denied.

“It is not intended to tie the fate of these five with that of the conference,” Mr. Hosseini said.

The head of the Iranian parliamentary committee on national security and foreign policy, Alaeddin Boroojerdi, also said Iran’s failure to participate in Sharm el-Sheik would lay the Islamic republic open to criticism from America.

“Iran should attend the conference, actively and powerfully,” Mr. Boroojerdi was quoted as saying by Iran’s official Islamic Republic News Agency.

Iran has considerable influence among Shiite parties in Iraq, who now lead the country’s government.

Iranian Foreign Minister Manouchehr Mottaki was expected to lead the delegation to Egypt, Mr. Hosseini told Iranian state television. America cut diplomatic ties with Iran following the 1979 storming of the American Embassy in Tehran. Although periodic diplomatic contacts have occurred, the Bush administration has resisted pressure at home and abroad to engage Iran in an effort to improve security in Iraq.

That policy began to change this spring. Although it is not inviting a broad conversation, the administration has repeatedly said it will not rule out sideline talks with either Iran or Syria.

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Associated Press writer Nasser Karimi in Tehran, Iran, contributed to this report.